Question: Solve for $x$ : $ 3|x - 1| - 2 = 5|x - 1| + 7 $
Subtract $ {3|x - 1|} $ from both sides: $ \begin{eqnarray} 3|x - 1| - 2 &=& 5|x - 1| + 7 \\ \\ {- 3|x - 1|} && {- 3|x - 1|} \\ \\ -2 &=& 2|x - 1| + 7 \end{eqnarray} $ Subtract $7$ from both sides: $ \begin{eqnarray} -2 &=& 2|x - 1| + 7 \\ \\ {- 7} && {- 7} \\ \\ -9 &=& 2|x - 1| \end{eqnarray} $ Divide both sides by ${2}$ $ \dfrac{-9} {{2}} = \dfrac{2|x - 1|} {{2}} $ Simplify: $ -\dfrac{9}{2} = |x - 1| $ The absolute value cannot be negative. Therefore, there is no solution.